Track-etched polycarbonate membranes (PC-TeMs) offer a structurally supported and well-defined nanoporous architecture, but their intrinsically low ionic conductivity limits their direct application as solid-state electrolytes in supercapacitors. Here, we grafted poly(acrylic acid) (PAA) into the cylindrical nanopores of PC-TeMs via reversible addition–fragmentation chain-transfer (RAFT) polymerization, incorporating graphene oxide (GO) at 0–1 wt% to enhance ion transport and structural stability. Structural, spectroscopic, and morphological analyses indicated effective PAA grafting along the nanochannels and homogeneous GO dispersion within the membrane matrix. Electrochemical tests revealed a non-linear dependence of performance on GO content: an optimal GO content of 0.5 wt% with PAA grafting delivered the highest ionic conductivity (0.57 mS·cm⁻¹) and specific capacitance (1.14 F·g⁻¹ at 5 mV·s⁻¹). This corresponds to improvements of approximately ~6× and ~800× compared to the ungrafted GO-free membrane (0.09 mS·cm⁻¹ and 1.42 mF·g⁻¹), and ~3× and ~42× compared to the ungrafted GO-containing membrane (0.18 mS·cm⁻¹ and 26.96 mF·g⁻¹), respectively. In contrast, at a GO content of 1 wt%, pore blockage and a decline in performance were observed. These results demonstrate that finely tuned GO incorporation into RAFT-grafted PAA/PC-TeMs enables dimensionally stable solid-state electrolytes for high-performance solid-state supercapacitors.